Elliptic curve isogeny class 50176.1-i over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-50176.1-i
• Conductor: 50176.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-1}) \)

Generator \(i\), with minimal polynomial \( x^{2} + 1 \); class number \(1\).

Elliptic curves in class 50176.1-i over \(\Q(\sqrt{-1}) \)

Isogeny class 50176.1-i contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
50176.1-i1	\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -5456 i\) , \( -111840 i + 111840\bigr] \)
50176.1-i2	\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -16 i\) , \( 32 i - 32\bigr] \)
50176.1-i3	\( \bigl[0\) , \( i + 1\) , \( 0\) , \( 144 i\) , \( -736 i + 736\bigr] \)
50176.1-i4	\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -1136 i\) , \( -8928 i + 8928\bigr] \)
50176.1-i5	\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -336 i\) , \( 1568 i - 1568\bigr] \)
50176.1-i6	\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -87376 i\) , \( -7058656 i + 7058656\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph